A criterion of fracture under proportional straining has been derived for materials that undergo plastic deformation prior to failure. This has been done using endochronic theories of plasticity and fracture proposed by Valanis. The strain criterion for fracture of brittle materials, proposed by Wu, falls into the class of more specific criteria encompassed by the criterion proposed here. The criterion suggests that fracture will occur when the magnitude s of the strain vector in strain space reaches a critical value. More specifically, in the event that s depends only on the angle PH 1 between the strain vector and hydrostatic strain vector, it then follows that s = s PH 1 thus giving rise to a polar form of a fracture surface which is rotationally symmetric with respect to hydrostatic strain vector. This polar form allows for a one parameter representation of the fracture surface in a triaxial strain field. In Part II of this paper it is shown that the theory is fully corroborated by extensive experimental data on gray cast iron.